如图,已知AB=AC,AD=AE,∠EAD=∠CAB,BD与CD相较于点O,求证说明:BD=CE.

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如图,已知AB=AC,AD=AE,∠EAD=∠CAB,BD与CD相较于点O,求证说明:BD=CE.
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如图,已知AB=AC,AD=AE,∠EAD=∠CAB,BD与CD相较于点O,求证说明:BD=CE.
如图,已知AB=AC,AD=AE,∠EAD=∠CAB,BD与CD相较于点O,求证说明:BD=CE.

如图,已知AB=AC,AD=AE,∠EAD=∠CAB,BD与CD相较于点O,求证说明:BD=CE.
证明:
∵∠EAD=∠CAB
∴∠EAD+∠CAD=∠CAB+∠CAD
即∠EAC=∠DAB
又∵AB=AC,AD=AE
∴△ABD≌△ACE(SAS)
∴BD=CE